{"paper":{"title":"Generalized Yetter-Drinfeld modules, the center of bi-actegories and groupoid-crossed braided bicategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Joost Vercruysse, Ryan Aziz","submitted_at":"2025-07-11T16:21:54Z","abstract_excerpt":"We study the notion of the $E$-center $\\mathcal{Z}_E(\\mathcal{M})$ of a $(\\mathcal{C}, \\mathcal{D})$-biactegory (or bimodule category) $\\mathcal{M}$, relative to an op-monoidal functor $E: \\mathcal{C} \\to \\mathcal{D}$. Specializing this notion to the case $\\mathcal{M} = {}_A\\mathrm{Mod}$, $\\mathcal{C}={}_H\\mathrm{Mod}$, $\\mathcal{D} = {}_K\\mathrm{Mod}$, and $E \\simeq C\\otimes_H - : {}_H\\mathrm{Mod} \\to {}_K\\mathrm{Mod}$, where $H$ and $K$ are bialgebras, $A$ is an $(H,K)$-bicomodule algebra and $C$ is a $(K,H)$-bimodule coalgebra, we show that this $E$-center is equivalent to the category of g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08722","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08722/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}